Imagine the statement:
- "I think that a racoon got into my neighbor's garbage last night."
Assume I am making the statement based on the spilled garbage on her driveway, my knowledge of the behavior of racoons, and previous sightings of racoons in the neighborhood. However, I have not proved it to be true -- I did not catch the little furry bandit in flagrante delicto, as it were; thus the statement has not been proven true. There are other possibilities -- feral cats, dogs, coyotes, opossums, etc. On the other hand, the statement is not false merely because it is unproven. It is merely unknown, with a strong probability in favor of the racoon hypothesis.
Up until a few months ago, the Higgs boson was an unproven hypothesis, which like the putative racoon, seemed a probable explanation; now scientists have discovered it.
What's wrong with your argument is that many statements are probable or hypothetical rather than proven or unproven.